It turns out that the "more CO2 = more warmer" model is hilariously simplified, and the real modelling gets into the weeds to put it mildly! There's a NASA database of the super-high-resolution absorption and emission spectra of every isotopic combination of every common molecule and ions, excited states, and more! It turns out that most of the forcing is determined by the behaviour of the upper atmosphere at high latitudes where the air is so thin that exotic excited states can persist for appreciable durations, and are made in large amounts by absorption of UV light. The "glancing angle" of the sunlight near the poles also means that even minor constituents participate in the exchange of IR radiation. Then, then, the simulation has to be run in many thin slices because air is so opaque to IR radiation that it bounces many times on the way up and down, and of course, the isotopic mixes (and excited fractions) are inconsistent between layers.
An insanely complex supercomputer model is required to come up with even a rough estimate of the actual warming.